Some integrated electronic circuits may utilize electronic resistors for proper operation. For example, a circuit for measuring an electrical current may be simplified by measuring the voltage drop across a resistor through which the test current is flowing. The latter approach may prove more economical than methods of measuring the current directly. However, the accuracy of this approach is limited to the accuracy of the resistor, per Ohm's Law.
In one approach, a length of doped polysilicon may be deposited on a substrate and contacts made at the ends of the length to form a resistor. Such approach may be relatively temperature stable with a low process variation. However, large polysilicon resistors occupy a large wafer area and may thus be expensive to implement. For example, a polysilicon resistor of 50 meg ohms may occupy a surface area on the order of 100,000 μm squared.
Another approach to integrated resistor implementation is that of using a MOS transistor operating in the linear region. The relationship between current I(D) through the drain-to-source channel of a MOS transistor operating in the linear region and the voltage V(DS) across the channel is given by:
            I      ⁡              (        D        )              =          k      ⁢                          ⁢                        W          L                ⁡                  [                                    V              ⁡                              (                GS                )                                      -                          V              ⁡                              (                TH                )                                      -                                          V                ⁡                                  (                  DS                  )                                            /              2                                ]                    ⁢              V        ⁡                  (          DS          )                      ,where k, W, and L are process and geometry dependent constants and V(TH) is the threshold voltage.
A resistance formed by the drain-to-source channel is thus represented as:
                              R          ⁡                      (            DS            )                          =                              V            ⁡                          (              DS              )                                            I            ⁡                          (              D              )                                                              =                  1                      k            ⁢                                                  ⁢                                          W                L                            ⁡                              [                                                      V                    ⁡                                          (                      GS                      )                                                        -                                      V                    ⁡                                          (                      TH                      )                                                        -                                                            V                      ⁡                                              (                        DS                        )                                                              /                    2                                                  ]                                                        
Unfortunately it can be seen that, for a given process and geometry, the resistance associated with a resistor formed using a MOS transistor operating in the linear region is not constant. The resistance of the MOS resistor so formed varies as a function of gate voltage and drain-to-source voltage.